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- W334017974 abstract "One-dimensional self-gravitating isothermal systems are stable with respect to one- dimensional perturbations. Let there be a number of parallel, infinite sheets between two parallel wails a distance 2l apart. Each sheet has the same uniform density and I is either finite or infinite. The sheets attract each other and move in one direction, x, bouncing against each other. The collision of two sheets is as though there were no collision at all, because they exchange their momenta. The system, however, is not collisionless since three sheets may also collide, Unbounded collisionless systems are well known to be stable with respect to perturbations in the x-direction (Feix et al., 1972). About unbounded collisional systems one knows that they are Jeans stable in the x-direction (Ledoux, 1951). Jeans instabilities appear for perturbations in the plane of the sheets. We shall show that both bounded and unbounded collisional systems are stable with respect to any other type of perturbation in the x-direction. Isothermal systems are in thermodynamic equilibrium; their thermodynamic potential is extremal. If the potential is maximal,/the system is stable with respect to any perturbation in the x-direction. Stability conditions in gravitating systems depend on how the system is constrained. However, all constrained systems will be stable if the least constrained system is stable because constraints do not destabilize a stable system.t The least constrained system may, of course, be unrealistic, but this is beside the point. Thus isothermal systems are stable if the thermodynamic potential of the least constrained system is maximum. The isothermal distribution is of the form" @default.
- W334017974 created "2016-06-24" @default.
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- W334017974 date "1980-01-01" @default.
- W334017974 modified "2023-09-27" @default.
- W334017974 title "A NOTE ON THE STABILITY OF ONE-DIMENSIONAL SELF-GRAVITATING ISOTHERMAL SYSTEMS (Letter to the Editor)" @default.
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